Consider a couple of functions (f,g) whose domain of definition is [-1,1]2 (i.e., the unit square).
Therefore, there must be a "wall" separating the left from the right, along which f is 0 (green curve inside the square).
Similarly, there must be a "wall" separating the top from the bottom, along which g is 0 (red curve inside the square).
The simplest generalization, as a matter of fact a corollary, of this theorem is the following one.
Then there is a point in the unit cube in which for all i: This statement can be reduced to the original one by a simple translation of axes, where By using topological degree theory it is possible to prove yet another generalization.